# ShapeFit and ShapeKick for Robust, Scalable Structure from Motion

arXiv: https://arxiv.org/abs/1608.02165 · HTML: https://mlsanity.com/paper/1608.02165/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2016.

## Built on by (most cited first, 16 of 16)

- [PreSight: Enhancing Autonomous Vehicle Perception with City-Scale NeRF Priors](https://mlsanity.com/paper/2403.09079/) (2024)
- [A Pose-only Solution to Visual Reconstruction and Navigation](https://mlsanity.com/paper/2103.01530/) (2021)
- [Hybrid Rotation Averaging: A Fast and Robust Rotation Averaging Approach](https://mlsanity.com/paper/2101.09116/) (2021)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Distributed Global Structure-from-Motion with a Deep Front-End](https://mlsanity.com/paper/2311.18801/) (2023)
- [AdaSfM: From Coarse Global to Fine Incremental Adaptive Structure from Motion](https://mlsanity.com/paper/2301.12135/) (2023)
- [Efficient Detection of Long Consistent Cycles and its Application to Distributed Synchronization](https://mlsanity.com/paper/2407.04260/) (2024)
- [Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor](https://mlsanity.com/paper/2409.09313/) (2024)
- [Cycle-Sync: Robust Global Camera Pose Estimation through Enhanced Cycle-Consistent Synchronization](https://mlsanity.com/paper/2511.02329/) (2025)
- [A Taxonomy of Structure from Motion Methods](https://mlsanity.com/paper/2505.15814/) (2025)
- [Solving Viewing Graph Optimization for Simultaneous Position and Rotation Registration](https://mlsanity.com/paper/2108.12876/) (2021)
- [PRAGO: Differentiable Multi-View Pose Optimization From Objectness Detections](https://mlsanity.com/paper/2403.08586/) (2024)
- [QuadSync: Quadrifocal Tensor Synchronization via Tucker Decomposition](https://mlsanity.com/paper/2602.22639/) (2026)
- [TriP: A Triangle Puzzle Approach to Robust Translation Averaging](https://mlsanity.com/paper/2605.07143/) (2026)
- [HETA++: Global Structure-from-Motion with Hybrid Explicit Translation Averaging](https://mlsanity.com/paper/2607.15912/) (2026)
- [Robust Global Structure-from-Motion via View Graph Pruning](https://mlsanity.com/paper/2608.22054/) (2026)

## Abstract (arXiv)

We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers. When pairwise directions represent scaled relative positions between pairs of views (estimated for instance with epipolar geometry) our method can be used for location recovery, that is the determination of relative pose up to a single unknown scale. For this task, our method yields performance comparable to the state-of-the-art with an order of magnitude speed-up. Our proposed numerical framework is flexible in that it accommodates other approaches to location recovery and can be used to speed up other methods. These properties are demonstrated by extensively testing against state-of-the-art methods for location recovery on 13 large, irregular collections of images of real scenes in addition to simulated data with ground truth.